I have used GNU/Linux for over a year on various distributions. I have done everything from edit text, programming, gaming, emulating, and modifying the look and feel of the desktop environment. To do so, I used a variety of useful tools which I will list below.
1 - GNU C Compiler
The GNU C Compiler, or GCC for short, allows you to compile programs written in the C programming language with gcc and C++ programming languages with g++. Non-programmers will also benefit from having gcc on their system, since a lot of the software mentioned will not come in a compiled package, so you must do it yourself.
sudo apt/yum/equo install gcc
2 - Firefox
Although not specific to gnu/linux, firefox is arguably the best web browser available. Firefox is free and open source, so anybody can edit and modify it to their needs. Firefox is also built on top of the second best plugin framework around (first being Eclipse), so it is highly extensible.
sudo apt/yum/equo install firefox
3 - Terminator
sudo apt/yum/equo install terminator
On most distros, xterm is the default terminal emulator. Terminator is a new terminal emulator with much added functionality, such as terminal groups and broadcasting.
4 - The Libreoffice suite
The Libreoffice suite can be seen as the open-source version of the Microsoft office suite, allowing the user to create presentations, documents, spreadsheets, databases, and drawings. Downloads are available at their website.
5 - zsh
Zsh, the Z-shell, is a replacement for BASH, the shell that is commonly found on Linux systems. Zsh brings multiple improvements to batch, especially with its advanced tab completion. Some of the attractions to zsh are its portability (since it doesn't rely on external programs), its backwards-compatibility with BASH, and the way it handles tab completion.
sudo apt/yum/equo install zsh
6 - GIMP
GIMP, the GNU Image Manipulation Program, is a photo editing program much like Photoshop. A debate continues to this day over which is better, but the fact that there is even question over which is superior is a telltale sign of GIMP's functionality. In the next major release, GIMP will become much easier to use and add additional features. That version of GIMP is available on Github right now.
sudo apt/yum/equo install gimp
7 - Avast Antivirus
Avast offers a free (gratis) antivirus program that can scan Linux systems for viruses. Although Linux is a very secure operating system, it has it's security holes. The primary usage for avast isn't for scanning your own system, but for scanning files you are planning on giving to another person.
8 - vim
Vim is a text editor that runs from the command line. It is a vast improvement over its predecessor, vi, in multiple ways. It supports plugins, has syntax highlighting right out of the box, and has a more logical (and less painful) command system than emacs.
sudo apt/yum/equo install vim
8 - tint2
This program may seem trivial, but if you are using another dock such as gnome-panel or cairo-dock you may want to check this out. I used to use docky, but it was heavyweight and requires composting. Tint2, in contrast, is lightweight, simple, and attractive. It could also save you some time. Right clicking on a window will close it instead of bringing up a menu.
sudo apt/yum/equo install tint2
9 - mplayer2
Whenever I'm not doing something that requires too much concentration, I listen to music. Although, I found myself wondering why I needed a GUI to do so. mplayer2 allows you to play music and watch videos from the command line. It also supports playlists and streaming.
sudo apt/yum/equo install mplayer2
10 - Links2
While we're still on the theme of command line applications, I must mention links2. Links2 is an improvement over links and lynx, and allows the browsing of the web through the command line. In addition to browsing, links can also handle the downloading of files. With links2 there is also an extremely fast, graphical browser that supports pictures.
sudo apt/yum/equo install links2
There are programs I have not mentioned that I use every day, such as picasa and code::blocks, but I did not mention them since they wouldn't appeal to everybody.